Problem: At the moment a hot iron rod is plunged into freezing water, the difference between the rod's and the water's temperatures is $100\degree$ Celsius. This causes the iron to cool and the temperature difference drops by $60\%$ every second. Write a function that gives the temperature difference in degrees Celsius, $D(t)$, $t$ seconds after the rod was plunged into the water. $D(t)=$
Solution: Dropping at a rate of $60\%$ per second means the temperature difference keeps $100\%-60\%=40\%$ of its value each second. So each second, the difference is multiplied by $40\%$, which is the same as a factor of $0.4$. If we start with the initial temperature difference, $100\degree$ Celsius, and keep multiplying by $0.4$, this function gives us the temperature difference $t$ seconds after the rod was plunged into the water: $D(t)=100(0.4)^t$